The Cross-Temporal Stability of Sex Differences in Piaget’s Water Level Tasks: A Meta-Analytical Multiverse

The Water Level Tasks (WLTs) were originally developed by Jean Piaget to examine children’s understanding of horizontality invariance and have since been widely used as a measure of spatial perception in adults. Piaget assumed that this task should be universally mastered by around the age of nine, thus reflecting the progression of concrete operational thought. However, subsequent research has shown that even some adults have substantial difficulties in correctly solving these tasks and indicated better performance of men compared to women. This sex effect has been often replicated, although its generality remains unclear. To address this gap, we synthesized all available evidence of WLT sex differences from 1964 to 2025 (261 independent samples comprising more than 37,000 participants) by means of a random-effects meta-analysis. To examine the generality of the observed meta-analytical summary effect across potential moderators, we conducted subgroup analyses and precision-weighted meta-regressions. Moreover, we performed meta-analytic specification curve and combinatorial meta-analyses, accounting for all reasonable as well as possible ways of which data to meta-analyze and how to meta-analyze them. Results indicated moderately-sized sex differences in WLT performance favoring men (d = 0.52) that increased with age but diminished over time. Specification curve analyses suggested stability of these sex differences across different test formats, sample characteristics, and meta-analytic model specifications, thus indicating a remarkable generality of this effect. In all, we show that WLT-based sex differences favoring men are moderate and robust but cross-temporally declining. In contrast to Piaget’s assumption of a universal understanding of horizontality invariance by late childhood as measured by the WLT, women are outperformed by men in solving this seemingly simple task.